為什么要改進成C4.5算法

原理

C4.5算法是在ID3算法上的一種改進，它與ID3算法最大的區別就是特征選擇上有所不同，一個是基于信息增益比，一個是基于信息增益。

之所以這樣做是因為信息增益傾向于選擇取值比較多的特征(特征越多，條件熵(特征劃分后的類別變量的熵)越小，信息增益就越大)；因此在信息增益下面加一個分母，該分母是當前所選特征的熵，注意：這里而不是類別變量的熵了。

這樣就構成了新的特征選擇準則，叫做信息增益比。為什么加了這樣一個分母就會消除ID3算法傾向于選擇取值較多的特征呢？

因為特征取值越多，該特征的熵就越大，分母也就越大，所以信息增益比就會減小，而不是像信息增益那樣增大了，一定程度消除了算法對特征取值范圍的影響。

實現

在算法實現上，C4.5算法只是修改了信息增益計算的函數calcShannonEntOfFeature和最優特征選擇函數chooseBestFeatureToSplit。

calcShannonEntOfFeature在ID3的calcShannonEnt函數上加了個參數feat，ID3中該函數只用計算類別變量的熵，而calcShannonEntOfFeature可以計算指定特征或者類別變量的熵。

chooseBestFeatureToSplit函數在計算好信息增益后，同時計算了當前特征的熵IV，然后相除得到信息增益比，以最大信息增益比作為最優特征。

在劃分數據的時候，有可能出現特征取同一個值，那么該特征的熵為0，同時信息增益也為0(類別變量劃分前后一樣，因為特征只有一個取值)，0/0沒有意義，可以跳過該特征。

#coding=utf-8import operatorfrom math import logimport timeimport os, sysimport stringdef createDataSet(trainDataFile): print trainDataFile dataSet = [] try: fin = open(trainDataFile) for line in fin:  line = line.strip()  cols = line.split('/t')  row = [cols[1], cols[2], cols[3], cols[4], cols[5], cols[6], cols[7], cols[8], cols[9], cols[10], cols[0]]  dataSet.append(row)  #print row except: print 'Usage xxx.py trainDataFilePath' sys.exit() labels = ['cip1', 'cip2', 'cip3', 'cip4', 'sip1', 'sip2', 'sip3', 'sip4', 'sport', 'domain'] print 'dataSetlen', len(dataSet) return dataSet, labels#calc shannon entropy of label or featuredef calcShannonEntOfFeature(dataSet, feat): numEntries = len(dataSet) labelCounts = {} for feaVec in dataSet: currentLabel = feaVec[feat] if currentLabel not in labelCounts:  labelCounts[currentLabel] = 0 labelCounts[currentLabel] += 1 shannonEnt = 0.0 for key in labelCounts: prob = float(labelCounts[key])/numEntries shannonEnt -= prob * log(prob, 2) return shannonEntdef splitDataSet(dataSet, axis, value): retDataSet = [] for featVec in dataSet: if featVec[axis] == value:  reducedFeatVec = featVec[:axis]  reducedFeatVec.extend(featVec[axis+1:])  retDataSet.append(reducedFeatVec) return retDataSet def chooseBestFeatureToSplit(dataSet): numFeatures = len(dataSet[0]) - 1 #last col is label baseEntropy = calcShannonEntOfFeature(dataSet, -1) bestInfoGainRate = 0.0 bestFeature = -1 for i in range(numFeatures): featList = [example[i] for example in dataSet] uniqueVals = set(featList) newEntropy = 0.0 for value in uniqueVals:  subDataSet = splitDataSet(dataSet, i, value)  prob = len(subDataSet) / float(len(dataSet))  newEntropy += prob *calcShannonEntOfFeature(subDataSet, -1) #calc conditional entropy infoGain = baseEntropy - newEntropy 　　 iv = calcShannonEntOfFeature(dataSet, i) if(iv == 0): #value of the feature is all same,infoGain and iv all equal 0, skip the feature continue 　　 infoGainRate = infoGain / iv if infoGainRate > bestInfoGainRate:  bestInfoGainRate = infoGainRate  bestFeature = i return bestFeature  #feature is exhaustive, reture what you want labeldef majorityCnt(classList): classCount = {} for vote in classList: if vote not in classCount.keys():  classCount[vote] = 0 classCount[vote] += 1 return max(classCount)   def createTree(dataSet, labels): classList = [example[-1] for example in dataSet] if classList.count(classList[0]) ==len(classList): #all data is the same label return classList[0] if len(dataSet[0]) == 1: #all feature is exhaustive return majorityCnt(classList) bestFeat = chooseBestFeatureToSplit(dataSet) bestFeatLabel = labels[bestFeat] if(bestFeat == -1): #特征一樣，但類別不一樣，即類別與特征不相關，隨機選第一個類別做分類結果 return classList[0]  myTree = {bestFeatLabel:{}} del(labels[bestFeat]) featValues = [example[bestFeat] for example in dataSet] uniqueVals = set(featValues) for value in uniqueVals: subLabels = labels[:] myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels) return myTree def main(): if(len(sys.argv) < 3): print 'Usage xxx.py trainSet outputTreeFile' sys.exit() data,label = createDataSet(sys.argv[1]) t1 = time.clock() myTree = createTree(data,label) t2 = time.clock() fout = open(sys.argv[2], 'w') fout.write(str(myTree)) fout.close() print 'execute for ',t2-t1if __name__=='__main__': main()